SinФ=-12/13
cosФ=Base/hypotenus
(hy)^2-(perpendicular)^2=(base)^2=13^2-12^2=5
cosФ=-5/13
This is a multiplication of fractions. If the tank is 3/4 full, and the tank holds 14.5 gal, then we need to multiply 14.5 * 3/4 First, convert 14.5 to 14 1/2 = 29/2 as an improper fraction Now, we have 29/2 * 3/4 = 87/8 = 10 7/8 gal That's how much gas is in the tank now. However, we want to know how much is needed to fill the tank. That can be determined by subtracting 10 7/8 from the amount that the tank can hold when full, which is 14.5 or 14 1/2. 14 1/2 - 10 7/8 can be re-written using improper fractions 29/2 - 87/8 We need a common denominator, which is 8 116/8 - 87/8 = 29/8 = 3 5/8 gal That's how much is needed to fill the tank
Answer: the boy won 10 games
Step-by-step explanation:
Let's call B as the number of games won by the boy, and F as the number of games won by the father.
We know that, there is a total of 26 games:
B + F = 26.
We know that in each game won by the boy, he wins 8 cents, for every game that the father wins, the boy losses 5 cents, and we know that at the end of the 26 games, the boy did not win or lose any money, so we have:
B*8 + F*(-5) = 0.
Then we have a system of equations:
B + F = 26
8*B - 5*F = 0.
The first step is isolating one of the variables. Let's start isolating F in the first equation:
B + F = 26
F = 26 - B.
Now we can replace this in the second equation:
8*B - 5*F = 0
8*B - 5*(26 - B) = 0
8*B + 5*B - 5*26 = 0
13*B = 5*26
B = 5*26/13 = 5*2 = 10
So the boy won 10 games (then the father won the other 16 games)
Answer:
x+4/x-4
Step-by-step explanation:
=x/(x-4)+4/(x-4) [ l.c.m= (x-4)]
=x+4/x-4
9514 1404 393
Answer:
22/44
Step-by-step explanation:
The probability of black is the ratio of black cards to all cards. If the Ace and 2 are removed from each suit, there will be 11 of the 13 cards remaining. 2 suits are black, for a total of 2×11 = 22 black cards. Of course there are 4 suits altogether, for a total of 4×11 = 44 total cards. Then you have ...
P(black) = (black cards)/(total cards)
P(black) = 22/44
_____
You are expected to be familiar with the fact that a deck of 52 playing cards consists of 4 suits: diamonds, clubs, hearts, spades. Each suit has 13 cards, identified as Ace, 2, 3, ..., 10, Jack, Queen, King. The clubs and spades are black; the diamonds and hearts are red.
